Numerical Methods for Non-Newtonian Fluids: Special Volume (Handbook of Numerical Analysis)

Numerical Methods for Non-Newtonian Fluids: Special Volume
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The corresponding numerical algorithms are presented in mathematical detail. The advantage of the particle-pdf approach in avoiding the spurious chaotic sensitivity of the particle-exact approach is demonstrated for Debye shielding and sheath configurations. In essence, the continuum perspective makes implicit the distinctness of the particles, which circumvents the Lyapunov instability of the N -body PIC system. The cost of the particle-pdf approach is comparable to the baseline PIC simulation.

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In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two types of PDEs are considered. The first one is an elliptic PDE with a discontinuous and high-contrast coefficient. While the second one is a linear elasticity equation with discontinuous stress tensor.

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In both cases, we represent the solutions of the PDEs using the deep neural networks DNNs and formulate the PDEs into variational problems, which can be solved via the deep learning approach. To deal with inhomogeneous boundary conditions, we use a shallow neural network to approximate the boundary conditions. Instead of using an adaptive mesh refinement method or specially designed basis functions or numerical schemes to compute the PDE solutions, the proposed method has the advantages that it is easy to implement and is mesh-free. Finally, we present numerical results to demonstrate the accuracy and efficiency of the proposed method for interface problems.

For wave propagation problems, we derive a closed expression of Riemann solvers for an interface between two distinct physics models with anisotropic material properties. Fortunately, with a generalized wave impedance, the Riemann problems can be unifiedly solved in a compact and consistent way. Numerical results are verified and validated with analytical solution and independent numerical solvers.

Liquid droplets sliding along solid surfaces are a frequently observed phenomenon in nature, e. To model this situation, we use a phase field approach. The bulk model is given by the thermodynamically consistent Cahn—Hilliard Navier—Stokes model from [Abels et al. To model the contact line dynamics we apply the generalized Navier boundary condition for the fluid and the dynamically advected boundary contact angle condition for the phase field as derived in [Qian et al.

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In recent years several schemes were proposed to solve this model numerically. While they widely differ in terms of complexity, they all fulfill certain basic properties when it comes to thermodynamic consistency. However, an accurate comparison of the influence of the schemes on the moving contact line is rarely found. Therefore, we thoughtfully compare the quality of the numerical results obtained with three different schemes and two different bulk energy potentials.

Especially, we discuss the influence of the different schemes on the apparent contact angles of a sliding droplet. We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from O N 2 per time step to O N , for a system with N particles with binary interactions.

For one of the methods, we give a particle number independent error estimate under some special interactions. Then, we apply these methods to some representative problems in mathematics, physics, social and data sciences, including the Dyson Brownian motion from random matrix theory, Thomson's problem, distribution of wealth, opinion dynamics and clustering. Numerical results show that the methods can capture both the transient solutions and the global equilibrium in these problems.

This study introduces a new computational scheme for the linear evolution of internal gravity wave packets passing over strongly non-uniform stratifications and background flows as found, e. Focusing on linear dispersion, which is dominant at small wave amplitudes, the scheme describes general wave superpositions arising from wave reflections near strong variations of the background stratification. Thus, it complements WKB theory, which is restricted to nearly monochromatic waves but covers weakly nonlinear effects in turn.

One envisaged application of the method is the formulation of bottom-of-the-stratosphere starting conditions for ray tracing parameterizations that follow nonlinear gravity wave packets into the upper atmosphere. The paper first summarizes a multilayer method for the numerical solution of the Taylor—Goldstein equation. Borrowing ideas from Eliassen and Palm Geophys Publ —23, , the scheme is based on partitioning the atmosphere into several uniformly stratified layers.

This allows for analytical plane wave solutions in each layer, which are matched carefully to obtain continuously differentiable global eigenmode solutions. This scheme enables rapid evaluations of reflection and transmission coefficients for internal waves impinging on the tropopause from below as functions of frequency and horizontal wavenumber. The study then deals with a spectral method for propagating wave packets passing over non-uniform backgrounds. Such non-stationary solutions are approximated by superposition of Taylor—Goldstein eigenmodes.

With this initialization in place, the state of the perturbations at any given subsequent time is obtained by a single superposition of suitably phase-shifted eigenmodes, i. Comparisons of solutions for wave packet evolution with those obtained from a nonlinear atmospheric flow solver reveal that apparently nonlinear effects can be the result of subtle linear wave packet dispersion.

This paper presents an investigation of flow asymmetry around a slender body at high angles of attack. The paper investigated the numerical aspect of simulating such flows. The impact of three simulation parameters, including grid resolution, discretization scheme, and turbulent flow modeling, was assessed. It was shown that insufficient grid density resulted in highly dissipated solution. At high angles, where flow asymmetry is expected to develop around the body, the dissipation from poor grid resolution prevented the flow asymmetry.

At higher grid resolution, the solution demonstrated a switch between two bistable states. Two spatial discretization schemes, namely central and bounded, were tested in the course of this study. The results illustrated the necessity to use non-dissipative unbiased discretization schemes. Large eddy simulation was performed using two sub-grid-scale models in addition to a run without a model. The sub-grid-scale models generated similar results except for switching of asymmetry direction and the axial location of separation foci.

The study shows that grid resolution and solution scheme have a profound effect on the validity of the simulation of flow around slender bodies at high angles of attack. The study also showed that stringent grid requirements marginalized the effect of the sub-grid-scale model. Analysis was performed on mean and unsteady flow fields. The total normal force increased with increasing angle of attack.

Comparison of computed dominant frequencies with experiment showed an acceptable agreement. Several dominant modes were identified: very low-frequency mode, low-frequency mode, intermediate-frequency mode, and high-frequency mode. The modes were shown to develop with increasing angle of attack. Unlike traditional synthetic jet, this new proposed zero-net-mass-flux actuator has managed to divide the blowing phase and suction phase apart on different separation edges on the rear part of the body. Numerical simulation based on the large eddy simulation method is carried out on the near-wake flow to obtain both time-averaged and transient information of the flow field.

The effects of the new actuators on the flow topology, the static pressure distribution and the process of the flow are analyzed to understand the mechanism of the drag reduction. Overcoming the drawbacks of the synthetic jet, our new zero-net-mass-flux actuator has successfully reduced the aerodynamic drag by a maximum of We obtain linearized, BiGlobal thermoacoustic solutions in a pulse tube driven via an imposed mean temperature gradient. Here, the pulse tube is treated as a key unit of a thermoacoustic heat engine, in which the conversion of thermal energy to useful acoustic fluctuations occurs.

A primary goal of this work is to understand the hydrodynamic efficiency of the energy conversion process and how it depends upon some of the important operating parameters, including the geometry of the device which in the limit of long length-to-diameter ratio approaches the so-called narrow tube approximation. As this limit is frequently imposed in the wave propagation analyses of thermoacoustic devices, it is critical to investigate the physical connections of such a model to more realistic finite-length pulse tube configurations, which we do here.

The mean flow is quiescent with an analytic mean temperature profile that still models the necessary physical details of the hot heat exchanger and regenerator. The computed thermoacoustic oscillations are found to be globally stable, approaching neutral stability conditions at the narrow tube limit. In finite-length tubes, three distinct types of modes are identified and analyzed.

Here, within a linear framework, radial modes do appear to act as key enablers for longitudinal modes to be the primary carriers of acoustic energy from the pulse tube section, while the identified boundary modes, essentially numerical constructs, are ignored in the analysis. Further, a disturbance energy-based efficiency metric is constructed that provides mechanistic understanding of some of the key parameters in pulse tube operation.

For finite-length tubes, it shows oscillations of the first asymmetric mode to be the most efficient, while the axisymmetric perturbations dominate for longer tubes that eventually lead to the idealized plane wave propagation. In the present paper, the formation of an air bubble in a shear-thinning non-Newtonian fluid was investigated numerically. The enhanced solver could compute the surface tension force more accurately, and it was important especially at low capillary and Bond numbers due to the dominance of surface tension force relative to the other forces.

According to the results, for Newtonian fluids, there is a critical capillary number for a given Bond number, and for lower values of this critical number, no difference is observed between the bubble detachment volumes and also bubble detachment times. Similarly, the results indicated that for non-Newtonian fluids, if apparent capillary number obtained by apparent viscosity is less than the critical capillary number, the detachment volume is the same as the corresponding Newtonian case.

The velocity of the bubble during its formation in Newtonian and shear-thinning fluids was also studied. Moreover, the bubble formation and detachment characteristics such as instantaneous contact angle and necking radius were investigated for Newtonian and non-Newtonian liquids, and the shear-thinning effect was examined as well.

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The results indicated that changing the ambient fluid to a non-Newtonian liquid has no effect on the trend of the contact angle; however, the minimum contact angle has a higher value when the shear-thinning effect increases. The structure of a shock wave is investigated using the continuum hypothesis for steady one-dimensional flow of a viscous non-ideal gas under heat conduction.

The coefficients of viscosity and heat conductivity are assumed to be directly proportional to a power of the temperature and density of the gas. The simplified van der Waals equation of state for the non-ideal gas has been assumed in this work. Qualitative analysis of shock wave structure has been done in terms of singularity analysis, isoclines, and integral curves.

The exact and numerical solutions of shock structure equations are obtained under the quantitative analysis. The validation of solution is established by comparing the results in the literature Iannelli in Int J Numer Methods Fluids 72 2 —, The variation of normalized gas velocity, viscous stress, heat flux, and shock thickness have been investigated across shock transition zone with the non-idealness of the gas, temperature, and density exponents in the viscosity and heat conductivity of the gas and initial Mach number.

It is found that gas velocity decreases significantly with the increase in non-idealness parameter, temperature, and density exponent in the viscosity of the gas. Shock wave thickness decreases with the increase in the non-idealness of the gas under constant viscosity and heat conductivity but increase under variable gas properties.

The thickness of a shock wave decreases with the increase in the temperature exponent and increases with the increase in the density exponent. An integrated simulation of a Drosophila wing—body combination in hovering flight has been carried out in order to analyze the Lagrangian and Eulerian coherent structures. A parallel unstructured finite volume method based on an arbitrary Lagrangian—Eulerian ALE formulation has been initially validated for a flapping rectangular plate and then employed to solve the incompressible unsteady Navier—Stokes equations around a Drosophila wing—body combination.

A robust mesh deformation algorithm based on indirect radial basis function method is utilized at each time level while avoiding remeshing. Meanwhile, the Lagrangian coherent structures are investigated using finite-time Lyapunov exponent fields. In addition, the instantaneous velocity vectors and particle traces are presented along with the aerodynamic parameters including the force, moment and power for a wing—body combination.

Furthermore, a wing-only configuration is also investigated in order to show the body effects on aerodynamic loads. The numerical simulations are used to gain insight into the near wake topology as well as their correlations with the aerodynamic force generation. The present fully coupled ALE algorithm is shown to be sufficiently robust to deal with large mesh deformations seen in flapping wings and reveals highly detailed near wake topology which is very useful to study physics in biological flights and can also provide an effective tool for designing bio-inspired MAVs and MFIs.

The parabolized stability equations PSE are a ubiquitous tool for studying the stability and evolution of disturbances in weakly nonparallel, convectively unstable flows. The PSE method was introduced as an alternative to asymptotic approaches to these problems. More recently, PSE has been applied with mixed results to a more diverse set of problems, often involving flows with multiple relevant instability modes. We show that PSE is capable of accurately capturing only disturbances with a single wavelength at each frequency and that other disturbances are not necessarily damped away or properly evolved, as often assumed.

This limitation is the result of regularization techniques that are required to suppress instabilities arising from the ill-posedness of treating a boundary value problem as an initial value problem. These findings are valid for both incompressible and compressible formulations of PSE and are particularly relevant for applications involving multiple modes with different wavelengths and growth rates, such as problems involving multiple instability mechanisms, transient growth, and acoustics.

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Our theoretical results are illustrated using a generic problem from acoustics and a dual-stream jet, and the PSE solutions are compared to both global solutions of the linearized Navier—Stokes equations and a recently developed alternative parabolization. In the tropical atmosphere, weather and climate are influenced by dispersive equatorial waves and their coupling with water vapor, deep convection, and rainfall. The dominant mode of variability on intraseasonal time scales is the Madden—Julian Oscillation MJO , which is still not fully understood.

Here we investigate the question: Is the MJO a linearly stable wave or an unstable wave?

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Numerical Methods for Non-Newtonian Fluids - 1st Edition - ISBN: Special Volume View all volumes in this series: Handbook of Numerical Analysis. Editorial Reviews. Review. "This excellent volume gives a complete and up-to- date Numerical Methods for Non-Newtonian Fluids: Special Volume ( Handbook of Mathematical and numerical analysis of non-Newtonian fluid flow models.

The linearly stable i. Here, to assess the other alternative, nonlinearity is added to the model and allows the study of the linearly unstable MJO regime. Model simulations are performed and evaluated for their ability to generate MJO variability as well as the full spectrum of tropical variability such as convectively coupled equatorial waves CCEWs.

In simulations of unstable growth, nonlinear advection slows the growth, and the wave saturates with reasonable amplitude, structure, speed, and dynamics. Overall, both the stable and unstable MJOs appear to be reasonable and may arise in different situations due to different environmental conditions. The temporal evolution of the initial shock front and the low Mach regime produced behind the front due to the sudden introduction of a spherical, finite-size, low Biot number, uniformly heated energy source in a variable property gas is investigated.

While the sphere is of physical interest, analogous problems of a uniformly heated infinitely long cylindrical wire and an infinite plate are also studied. Compressibility, finite-size, and nonlinear heating effects are studied without constraining the temperature of the source. Shortly after the energy source is introduced, compressibility is significant and a strong shock wave forms which weakens as it moves away from the source eventually becoming an acoustic wave.

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I have also published an undergraduate text — Elements of Mathematics for Economics and Finance — which was published by Springer in Ontvang je nog geen nieuwsbrieven van ons? Fatigue of Materials and Structures. Articles MacKay, A. The method has been widely used by researchers and practitioners since Manabu Iguchi.

Behind it, fluid motion occurs at a much lower speed low Mach regime , where the resulting nonlinear heating problem is solved analytically using the method of homotopy perturbation expansion leading to weak decoupling of finite-size effects and nonlinear heating effects. Ayala, Lian-Ping Wang Abstract The interpolated bounce-back schemes and the immersed boundary method are the two most popular algorithms in treating a no-slip boundary on curved surfaces in the lattice Boltzmann method.

Bykov, A. Kiverin, A. Koksharov, I.

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Yakovenko Abstract The paper introduces the results of the validation of two contemporary CFD techniques for numerical analysis of transient combustion phenomena. Agarwal, Jian-Feng Chen Abstract Numerical simulations of a multiphase system synthesis of butyl rubber in a rotating packed bed RPB are reported in this paper.

Hamzah Abstract Heatlines visualization of natural convection heat transfer in trapezoidal-shape cavity filled with nanofluid TiO 2 -water and divided by horizontal porous media partition has been studied numerically using finite element method. Volume 33, Issue 4 , May , Page Summary This work studies the implementation of wall modeling for large eddy simulation in a finite element context. Summary This paper presents a continuous finite element solution for fluid flows with interfaces. Summary In this paper, simple and consistent open boundary conditions are presented for the numerical simulation of viscous incompressible laminar flows.

Summary The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. The interplay between deep learning and model reduction.

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Chung, Yalchin Efendiev, Mary Wheeler Abstract In this paper, we investigate neural networks applied to multiscale simulations of porous media flows and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Publication date: Available online 24 September Source: Journal of Computational Physics Author s : Dong Liang, Zhongguo Zhou Abstract In the paper, a new conservative splitting decomposition method S-DDM is developed for computing nonlinear multicomponent contamination flows in porous media over multi-block sub-domains.

Bond, Eric C. Cyr, Jonathan B. Freund Abstract Particle-in-cell PIC simulation methods are attractive for representing species distribution functions in plasmas. Publication date: Available online 23 September Source: Journal of Computational Physics Author s : Zhongjian Wang, Zhiwen Zhang Abstract In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach.

Publication date: Available online 19 September Source: Journal of Computational Physics Author s : Qiwei Zhan, Mingwei Zhuang, Yiqian Mao, Qing Huo Liu Abstract For wave propagation problems, we derive a closed expression of Riemann solvers for an interface between two distinct physics models with anisotropic material properties. Volume 20, Issue 6 , June , Page Physics of Fluids, Volume 31, Issue 9 , September The SHS comprised of streamwise or azimuthal microgrooves MG , spanwise or longitudinal MG, grooves inclined to the streamwise direction spiral , and microposts.

The SHS have been modeled as shearfree areas. We have tried to understand the role of the effective slip and modified turbulence dynamics responsible for DR by analyzing the statistics of mean flow, velocity fluctuations, Reynolds stresses, turbulence kinetic energy TKE , and near-wall streaks. Most of the results show enhanced production of near-wall streamwise velocity fluctuations and TKE resulting in near-wall turbulence enhancement, yet we observed DR for most of the cases, thereby implying slip to be the dominant contributor to DR in comparison to modified near-wall turbulence.

Nonlinear interaction and coalescence features of oscillating bubble pairs are investigated experimentally and numerically. The spark technique is used to generate in-phase bubble pairs with similar size and the simulation is performed with the compressible volume of fluid VOF solver in OpenFOAM. The initial conditions for the simulation are determined from the reference case, where the interbubble distance is sufficiently large and the spherical shape is maintained at the moment of maximum volume.

Although the microscopic details of the coalescing behaviors are not focused, the compressible VOF solver reproduces the important features of the experiment and shows good grid convergence. For Pattern I, prominent gas flow and velocity fluctuation can be observed in the coalescing region, which may induce the annular protrusion in the middle of the coalesced bubble. For Patterns II and III, migration of the bubbles toward each other during the collapsing and rebounding stages greatly facilitates the bubble coalescence.

The time evolution of the liquid-film thickness of a single cavitation bubble in water collapsing onto a solid surface is measured. To this end, total internal reflection TIR shadowmetry is developed, a technique based on TIR and the imaging of shadows of an optical structure on a polished glass surface. The measurements are performed at frame rates up to kHz.

Simultaneous high-speed imaging of the bubble shape at up to 89 kHz allows relating the evolution of the film thickness to the bubble dynamics. We find that during the first collapse phase, the bubble does not come in direct contact with the solid surface. Instead, when the bubble collapses, the jet impacts on a liquid film that always resides between the bubble and solid. Also, during rebound, at any given point in time, most or all of the then overall toroidal bubble is not in contact with the solid surface.

We have conducted large-eddy simulations of turbulent separated flows over a NACA airfoil with control by a plasma actuator.

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The Reynolds number based on the chord length is 1 , and the angle of attack is At this angle of attack, the flow around the airfoil is fully separated. The effects of the location and operating conditions of the plasma actuator on the separation control are investigated. The plasma actuator is set at the leading edge, the turbulent reattachment point, or near the turbulent separation point.

These frequencies are determined based on the dominant frequencies of the turbulent separated flow field of the no control case. A continuous actuation case has also been conducted. The location of the actuator where it most effectively suppresses the separation is the one closest to the turbulent separation point.

In the burst mode case, the nondimensional burst frequency of unity is most effective in terms of the increase in the lift. To clarify the effective control mechanism, five objectives for turbulent separation control are compared. The results show that it is difficult to suppress the turbulent separation using the same strategies as in laminar separation control. The effective mechanism for turbulent separation control by burst actuation is found to be inducing the pairing of large-scale vortices near the airfoil surface. This large-scale vortex pairing induces freestream momentum into the boundary layer, leading to separation suppression.

In addition, three other control effects can be achieved by varying the operating settings of the plasma actuator. The drag is slightly improved by reducing the length of the laminar separation bubble through high-frequency actuation from the leading edge. It is known from recent studies that evaporation induces flow around a droplet at atmospheric conditions.

This flow is visible even for slowly evaporating liquids like water. In the present study, we investigate the influence of the ambient gas on the evaporating droplet. We observe from the experiments that the rate of evaporation at atmospheric temperature and pressure decreases in a heavier ambient gas. The evaporation-induced flow in these gases for different liquids is measured using particle image velocimetry and found to be very different from each other. However, the width of the disturbed zone around the droplet is seen to be independent of the evaporating liquid and the size of the needle for the range of needle diameters studied , and only depends on the ambient gas used.

Deep Reinforcement Learning DRL has recently been proposed as a methodology to discover complex active flow control strategies [Rabault et al. However, while promising results were obtained on a simple 2-dimensional benchmark flow at a moderate Reynolds number, considerable speedups will be required to investigate more challenging flow configurations.

Therefore, speedups should be obtained through a combination of two approaches. The first one, which is well documented in the literature, is to parallelize the numerical simulation itself. The second one is to adapt the DRL algorithm for parallelization. Here, a simple strategy is to use several independent simulations running in parallel to collect experiences faster.

In the present work, we discuss this solution for parallelization. Solid State NMR. Jerry C. Molecular Magnetic Materials. Barbara Sieklucka. David Holcman. Trends in Applied Theoretical Chemistry. Rate Constant Calculation for Thermal Reactions. Herbert DaCosta. Kohei Miyata. Mihai V. The Sun, the Solar Wind, and the Heliosphere. Mari Paz Miralles. Richard C. Density-Functional Methods for Excited States. Modeling Marvels. Errol G. Gregory Voth. Ultrafast Dynamics at the Nanoscale. Stefan Haacke. Daniel Canet. Transient Effects in Friction. Andreas Goedecke. An Introduction to Fluid Dynamics.

Experimental and Theoretical Approaches to Actinide Chemistry. John K. Philip E. Statistical Thermodynamics and Stochastic Kinetics. Yiannis N. Flux-Corrected Transport. Dmitri Kuzmin. Ludovic Berthier. Zintl Phases. Thomas F. The Pi-Theorem. Ney A. Practical Aspects of Computational Chemistry I. Multiscale Molecular Methods in Applied Chemistry. Quantum Effects in Biology. Masoud Mohseni. Basic Transport Phenomena in Materials Engineering. Manabu Iguchi. The Mathematics and Topology of Fullerenes. Franco Cataldo. Igor Nesteruk. Michael McKee. Advances in Imaging and Electron Physics.

Peter W. Mathematical Modeling in Mechanics of Granular Materials. Oxana Sadovskaya. Mass Per Pettersson. Graham A. Diamond and Related Nanostructures. Mircea Vasile Diudea. Parallel Computational Fluid Dynamics ' Conducting and Magnetic Organometallic Molecular Materials. Thomas Carraro.

Anne E. Annual Reports in Computational Chemistry. Ralph A. Lectures on the Theory of Water Waves. Thomas J. Advances in Atomic, Molecular, and Optical Physics. Ennio Arimondo. Yuichi Hirai. Numerical Modeling of Sea Waves. Dmitry V. Fundamentals of Modern Unsteady Aerodynamics. Structure and Function. Peter Comba.

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The Lattice Boltzmann Method.